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Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations. (English) Zbl 1360.81176

81Q50 Quantum chaos
22E70 Applications of Lie groups to the sciences; explicit representations
20B30 Symmetric groups
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[1] Weingarten D 1978 Asymptotic behavior of group integrals in the limit of infinite rank J. Math. Phys.19 999 · Zbl 0388.28013
[2] Samuel S 1980 U(N) integrals, 1/N, and de Wit-’t Hooft anomalies J. Math. Phys.21 2695
[3] Mello P A 1990 Averages on the unitary group and applications to the problem of disordered conductors J. Phys. A: Math. Gen.23 4061
[4] Brouwer P W and Beenakker C W J 1996 Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems J. Math. Phys.37 4904 · Zbl 0861.22014
[5] Degli Esposti M and Knauf A 2004 On the form factor for the unitary group J. Math. Phys.45 4957 · Zbl 1064.81036
[6] Collins B 2003 Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability Int. Math. Res. Not.17 953 · Zbl 1049.60091
[7] Collins B and Śniady P 2006 Integration with respect to the Haar measure on unitary, orthogonal and symplectic group Commun. Math. Phys.264 773 · Zbl 1108.60004
[8] Collins B and Matsumoto S 2009 On some properties of orthogonal Weingarten functions J. Math. Phys.50 113516 · Zbl 1304.22007
[9] Zuber J-B 2008 The large-N limit of matrix integrals over the orthogonal group J. Phys. A: Math. Theor.41 382001 · Zbl 1147.82019
[10] Banica T, Collins B and Schlenker J-M 2011 On polynomial integrals over the orthogonal group J. Comb. Theory A 118 78 · Zbl 1227.05057
[11] Matsumoto S and Novak J 2013 Jucys-Murphy elements and unitary matrix integrals Int. Math. Res. Not.2 362 · Zbl 1312.05143
[12] Zinn-Justin P 2010 Jucys-Murphy elements and Weingarten matrices Lett. Math. Phys.91 119 · Zbl 1283.05269
[13] Matsumoto S 2013 Weingarten calculus for matrix ensembles associated with compact symmetric spaces Random Matrices: Theory Appl.2 1350001 · Zbl 1280.15020
[14] Scott A J 2008 Optimizing quantum process tomography with unitary 2-designs J. Phys. A: Math. Theor.41 055308 · Zbl 1141.81009
[15] Žnidarič M, Pineda C and García-Mata I 2011 Non-Markovian behavior of small and large complex quantum systems Phys. Rev. Lett.107 080404
[16] Cramer M 2012 Thermalization under randomized local Hamiltonians New J. Phys.14 053051
[17] Vinayak and Žnidarič M 2012 Subsystem’s dynamics under random Hamiltonian evolution J. Phys. A: Math. Theor.45 125204 · Zbl 1245.81065
[18] Novaes M 2013 A semiclassical matrix model for quantum chaotic transport J. Phys. A: Math. Theor.46 502002 · Zbl 1298.82062
[19] Novaes M 2015 Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry Ann. Phys.361 51 · Zbl 1360.81177
[20] Novaes M 2014 Elementary derivation of Weingarten functions of classical Lie groups (arXiv:1406.2182v2 [math-ph])
[21] Zinn-Justin P and Zuber J-B 2003 On some integrals over the U(N) unitary group and their large N limit J. Phys. A: Math. Gen.36 3173 · Zbl 1074.82013
[22] Collins B, Guionnet A and Maurel-Segala E 2009 Asymptotics of unitary and orthogonal matrix integrals Adv. Math.222 172 · Zbl 1184.15024
[23] Ginibre J 1965 Statistical ensembles of complex, quaternion, and real matrices J. Math. Phys.6 440 · Zbl 0127.39304
[24] Morris T R 1991 Chequered surfaces and complex matrices Nucl. Phys. B 356 703
[25] ’t Hooft G 1974 A planar diagram theory for strong interactions Nucl. Phys. B 72 461
[26] Bessis D, Itzykson C and Zuber J B 1980 Quantum field theory techniques in graphical enumeration Adv. Appl. Math.1 109 · Zbl 0453.05035
[27] Di Francesco P 2003 Rectangular matrix models and combinatorics of colored graphs Nucl. Phys. B 648 461 · Zbl 1005.82003
[28] Novaes M 2015 Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation J. Math. Phys.56 062109 · Zbl 1322.81049
[29] Bousquet-Mélou M and Schaeffer G 2000 Enumeration of planar constellations Adv. Appl. Math.24 337 · Zbl 0955.05004
[30] Irving J 2009 Minimal transitive factorizations of permutations into cycles Can. J. Math.61 1092 · Zbl 1186.05006
[31] Bouttier J 2011 Matrix integrals and enumeration of maps The Oxford Handbook of Random Matrix Theory ed G Akemann et al (Oxford: Oxford University Press) ch 26
[32] Berkolaiko G and Irving J 2016 Inequivalent factorizations of permutations J. Combin. Theory A 140 1-37 · Zbl 1331.05005
[33] Bóna M and Pittel B 2016 On the cycle structure of the product of random maximal cycles (arXiv:1601.00319v1)
[34] Bernardi O, Morales A, Stanley R and Du R 2014 Separation probabilities for products of permutations Comb. Probab. Comput.23 201 · Zbl 1290.05003
[35] Morales A H and Vassilieva E A 2010 Bijective evaluation of the connection coefficients of the double coset algebra (arXiv:1011.5001v1)
[36] Hanlon P J, Stanley R P and Stembridge J R 1992 Some combinatorial aspects of the spectra of normally distributed random matrices Contemp. Math.138 151 · Zbl 0789.05092
[37] Goulden I P and Jackson D M 1996 Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials Can. J. Math.48 569 · Zbl 0861.05062
[38] Matsumoto S 2011 Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures Ramanujan J.26 69 · Zbl 1233.05214
[39] Berkolaiko G and Kuipers J 2013 Combinatorial theory of the semiclassical evaluation of transport moments I: equivalence with the random matrix approach J. Math. Phys.54 112103 · Zbl 1288.81048
[40] Müller S, Heusler S, Braun P and Haake F 2007 Semiclassical approach to chaotic quantum transport New J. Phys.9 12
[41] Müller S, Heusler S, Braun P, Haake F and Altland A 2005 Periodic-orbit theory of universality in quantum chaos Phys. Rev. E 72 046207
[42] Berkolaiko G and Kuipers J 2013 Combinatorial theory of the semiclassical evaluation of transport moments II: algorithmic approach for moment generating functions J. Math. Phys.54 123505 · Zbl 1288.82053
[43] Novaes M 2012 Semiclassical approach to universality in quantum chaotic transport Europhys. Lett.98 20006
[44] Novaes M 2013 Combinatorial problems in the semiclassical approach to quantum chaotic transport J. Phys. A: Math. Theor.46 095101 · Zbl 1267.81171
[45] Macdonald I G 1995 Symmetric Functions and Hall Polynomials 2nd edn (Oxford: Oxford University Press)
[46] Friedman W A and Mello P A 1985 Marginal distribution of an arbitrary square submatrix of the S-matrix for Dyson’s measure J. Phys. A: Math. Gen.18 425 · Zbl 0572.60025
[47] Życzkowski K and Sommers H-J 2000 Truncations of random unitary matrices J. Phys. A: Math. Gen.33 2045 · Zbl 0957.82017
[48] Neretin Y A 2002 Hua-type integrals over unitary groups and over projective limits of unitary groups Duke Math. J.114 239 · Zbl 1019.43008
[49] Forrester P J 2006 Quantum conductance problems and the Jacobi ensemble J. Phys. A: Math. Gen.39 6861 · Zbl 1092.81069
[50] Fyodorov Y V and Khoruzhenko B A 2007 A few remarks on colour-flavour transformations, truncations of random unitary matrices, Berezin reproducing kernels and Selberg-type integrals J. Phys. A: Math. Theor.40 669 · Zbl 1183.81070
[51] Shen J 2001 On the singular values of Gaussian random matrices Linear Algebr. Appl.326 1 · Zbl 0985.15019
[52] Edelman A and Rao N R 2005 Random matrix theory Acta Numer.14 233 · Zbl 1162.15014
[53] Mehta M L 2004 Random Matrices (New York: Academic) ch 17
[54] Forrester P J and Warnaar S O 2008 The importance of the Selberg integral Bull. Am. Math. Soc.45 489 · Zbl 1154.33002
[55] Khoruzhenko B A, Sommers H-J and Życzkowski K 2010 Truncations of random orthogonal matrices Phys. Rev. E 82 040106
[56] Stanley R P 1999 (Enumerative Combinatorics vol 2) (Cambridge: Cambridge University Press) · Zbl 0928.05001
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